2. (a) When a particle of mass 1.0 x 10-26 g in a one-dimensional box goes...
2. (a) When a particle of mass 1.0 x 10-26 g in a one-dimensional box goes from the n=3 level to n=1 level, it emits a radiation with frequency 5.0 x 1014 Hz. Calculate the length of the box.
(b) Suppose that an electron freely moves around inside of a three-dimensional rectangular box with dimensions of 0.4 nm (width), 0.4 nm (length), and 0.5 nm (height). Calculate the frequency of the radiation that the electron would absorb during its transition from the ground state (the lowest energy state) to the first excited state (the second lowest energy state).
Homework Answers
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2. (a) When a particle of mass 1.0 x 10-26 g in a
one-dimensional box goes...
Assume that four electrons are confined to a one dimensional box 4.95 ✕ 10−10 m in...
Assume that four electrons are confined to a one dimensional box 4.95 ✕ 10−10 m in length. If two electrons can occupy each allowed energy level, calculate the wavelength of electromagnetic radiation necessary to promote the highest-energy electron into the first excited state.
An electron in a 10.1-nm one-dimensional box is excited from the ground state into a higher-energy...
An electron in a 10.1-nm one-dimensional box is excited from the ground state into a higher-energy state by absorbing a photon of electromagnetic radiation with a wavelength of 13,950 nm. Determine the final energy state for this transition. 04 0 0 w Na Un 0 0 1 pts Question 24
What is the length of a one-dimensional box if an electron requires a wavelength of 6350...
What is the length of a one-dimensional box if an electron requires a wavelength of 6350 nm to be excited from the n = 2 to the n = 3 energy level?
7. We have an electron trapped in a one dimensional box, and is excited to the...
7. We have an electron trapped in a one dimensional box, and is excited to the 2nd (n = 2) state. What will be the length of the box if our electron has the same energy as a violet photon (404 nm)?
1) Calculate the frequency of the photon that a particle has to absorb in a box...
1) Calculate the frequency of the photon that a particle has to absorb in a box to make a transition from the ground state. to the third excited level. 2) Calculate the average position of a particle in a box at the first excited level of energy.
4. An electron is in a one-dimensional box in the n-1 state. Its energy is equal...
4. An electron is in a one-dimensional box in the n-1 state. Its energy is equal to that of a 600 nm photon. a. What is the energy of the photon? b. What is the length of the box if the electron has the same energy of the photon? c. What is the lowest energy possible for a proton in this box?
Consider an electron in a one-dimensional box as a model of a quantum dot. Suppose the...
Consider an electron in a one-dimensional box as a model of a quantum dot. Suppose the box has width 0.7 nm. For this problem, absorption of light and subsequent relaxation connect two states (i andj) with a difference in energy, AEi E - E. (a) Calculate AEsi and AE2I for luminescence from excited energy levels to the ground state. Convert the energies to the corresponding wavelengths of light, λ31 and λ21. (b) Find the wavelength of light that corresponds to...
problems 7 & 8 Problem 7: A particle confined in a rigid one-dimensional box of length...
problems 7 & 8
Problem 7: A particle confined in a rigid one-dimensional box of length 1 x 10-14m has an energy level ER = 32 MeV and an adjacent energy level En+1 = 50 MeV. 1 MeV = 1 x 106 eV (a) Determine the values of n and n + 1. Answer: n = 4 and n+1 = 5. (b) What is the wavelength of a photon emitted in the n+1 to n transition? Answer: X = 6.9...
An electron is confined in the ground state in a one-dimensional box of width 10-10 m....
An electron is confined in the ground state in a one-dimensional box of width 10-10 m. Its energy is known to be 38 eV. (a) Calculate the energy of the electron in its first and second excited states (b) Sketch the wave functions for the ground state, the first and the second excited states (c) Estimate the average force (in Newtons) exerted on the walls of the box when the electron is in the ground state. (d) Sketch the new...
Model the electron in a hydrogen atom as a particle in a one-dimensional box with side...
Model the electron in a hydrogen atom as a particle in a one-dimensional box with side length 150 pm. What wavelength of radiation would be emitted when the electron falls from n=3 to n=2? Repeat the calculation for the transition from n=4 to n=2. Compare the results with the corresponding transitions for the Bohr model.
An electron in a 10.1-nm one-dimensional box is excited from the ground state into a higher-energy state by absorbing a photon of electromagnetic radiation with a wavelength of 13,950 nm. Determine the final energy state for this transition. 04 0 0 w Na Un 0 0 1 pts Question 24
7. We have an electron trapped in a one dimensional box, and is excited to the 2nd (n = 2) state. What will be the length of the box if our electron has the same energy as a violet photon (404 nm)?
4. An electron is in a one-dimensional box in the n-1 state. Its energy is equal to that of a 600 nm photon. a. What is the energy of the photon? b. What is the length of the box if the electron has the same energy of the photon? c. What is the lowest energy possible for a proton in this box?
Consider an electron in a one-dimensional box as a model of a quantum dot. Suppose the box has width 0.7 nm. For this problem, absorption of light and subsequent relaxation connect two states (i andj) with a difference in energy, AEi E - E. (a) Calculate AEsi and AE2I for luminescence from excited energy levels to the ground state. Convert the energies to the corresponding wavelengths of light, λ31 and λ21. (b) Find the wavelength of light that corresponds to...
problems 7 & 8
Problem 7: A particle confined in a rigid one-dimensional box of length 1 x 10-14m has an energy level ER = 32 MeV and an adjacent energy level En+1 = 50 MeV. 1 MeV = 1 x 106 eV (a) Determine the values of n and n + 1. Answer: n = 4 and n+1 = 5. (b) What is the wavelength of a photon emitted in the n+1 to n transition? Answer: X = 6.9...
An electron is confined in the ground state in a one-dimensional box of width 10-10 m. Its energy is known to be 38 eV. (a) Calculate the energy of the electron in its first and second excited states (b) Sketch the wave functions for the ground state, the first and the second excited states (c) Estimate the average force (in Newtons) exerted on the walls of the box when the electron is in the ground state. (d) Sketch the new...
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